This invention relates to video signal processing where a signal in digitally-sampled form is subjected to a non-linear processing operation, and to reducing certain subjective impairments introduced by such processing.
FIG. 1 shows, in rudimentary form, those features of a normal analogue television system that provide a helpful introduction to understand the environment of this invention.
The light from a scene is imaged onto a sensor 21 where it is scanned. The electrical signal from this sensor is low-pass filtered in a filter 23 and passes to a gamma corrector 25, the purpose of which will be described later. The gamma-corrected signal is then low-pass filtered in a channel filter 27 to restrict the bandwidth to that available in the transmission channel. The signal received from the channel passes to a display 29 where it is converted back to an optical image of the original scene.
The transfer characteristics between the electrical signal into a cathode ray tube such as used in the display 29 and the light given out by the tube are far from linear. Indeed when the operating conditions have been set correctly the light output is closely proportional to the input when it has been raised to a constant power, or index. This power-law constant is called the gamma of the display tube. Historically, it used to be about 2.2 but current colour displays have a gamma that is higher, typically in the range 2.4 to 2.8. This spread of gamma is due to variations between different types of display tube although for each type it is substantially constant.
Although in many ways it would be better if the display tube were linear, i.e. gamma equal to 1, the non-linearity is useful in one most important respect, in that it causes channel noise to be more or less equally disturbing in all shades of grey between black and white. If the tube were linear the effect of channel noise in the darker areas would be very much worse.
If no correction were introduced for the effects of display gamma, the details in the shadow areas would be very much suppressed and the effect on colour would be equally severe. Although the corrector in theory should have a power of 1/gamma to achieve the same contrast ratio on the display as occurred in the scene, experience shows that the displayed pictures look better if the contrast ratio displayed is somewhat higher than that of the original scene. If the product of the powers of the gamma corrector and the display gammas is about 1.2, this seems to be about optimum, causing a preferred increase of displayed contrast and colour saturation.
In a telecine the film being scanned may also have an increased contrast or gamma and in this case the gamma correction will be required not only for the display but also for the characteristics of the film.
The gamma correction is a non-linear operation and thus produces harmonics, but it is found that the removal of these by the channel filter 27 is rarely noticeable, although it is undesirable from theoretical considerations.
FIG. 2 shows how part of the previous figure is changed when digital gamma correction is used. The boxes 33, 35 and 37 perform essentially the same function as boxes 23, 25 and 27, respectively, in the case of the analogue gamma correction in the circuit of FIG. 1. However, the cut-off rate of the filters may need to be slightly sharper for the digital implementation and of course the gamma correction itself is realised digitally, most simply by using the video as the address to interrogate a Read Only Memory (ROM) which has been suitably programmed. Two new boxes have been introduced, an analogue-to-digital converter 34 between the low pass filter 33 and the gamma corrector 35, and a digital-to-analogue converter 36 between the gamma corrector 35 and the channel filter 37.
The normal Nyquist requirement is to sample at a frequency which is greater than twice the highest possible signal frequency. For example, if the desired response requires that the filters 33 and 37 be flat to 5.5 MHz and if they also cut-off rapidly, being 12 or more decibels down at 6.75 MHz, this would be suitable for the normal case of a sampling frequency of 13.5 MHz. Since there are two filters, a 12 dB attenuation at half the sampling frequency per filter will, with typical filters, result in the alias components being attenuated by at least twice this amount, or 24 dB. However, the situation is not normal, as gamma correction is not a linear operation. The law of the gamma correction is required to be the same for analogue and digital realisations so the digital words at the output of the corrector 35 in FIG. 2, would be identical to those which would appear at the output of A/D converter 44 in FIG. 3. In FIG. 3 the positions of the A/D converter and the gamma corrector are interchanged, so that the gamma corrector is operating with analogue signals. By this means it is possible to compute the possible alias effects which can arise with the circuit of FIG. 2. The unit part of the box numbers in FIGS. 2 and 3 are the same for the same type of box, the numbers being increased by ten.
The level of alias effects will depend on the amplitude of the harmonics produced by the non-linearity of the gamma correction and on their frequency. In Table 1 it is assumed that the maximum peak-to-peak (p-p) amplitude of the signal is 1. The left hand column gives the peak-to-peak amplitude of a sine wave superimposed on a direct component of 0.5v. To the right, successive columns show the direct component, and the peak amplitudes of the fundamental and of each of the second, third and fourth harmonics appearing at the output of the gamma corrector. The table assumes a correction gamma value of 0.4, corresponding to a display gamma of 2.5.
TABLE 1 ______________________________________ Direct 2nd 3rd 4th Input p-p cpt. Fundamental harm. harm. harm. ______________________________________ 1.000 0.6795 0.3883 -0.0971 0.0457 -0.0270 0.875 0.7113 0.3032 -0.0516 0.0159 -0.0060 0.750 0.7271 0.2477 -0.0329 0.0078 -0.0023 0.625 0.7379 0.2001 -0.0208 0.0039 -0.0009 0.500 0.7457 0.1566 -0.0125 0.0018 -0.0003 0.375 0.7512 0.1157 -0.0067 0.0007 -0.0001 0.250 0.7550 0.0764 -0.0029 0.0002 -0.0000 0.125 0.7571 0.0380 -0.0007 0.0000 -0.0000 0.000 0.7579 0.0000 -0.0000 0.0000 -0.0000 ______________________________________
From the above Table it can be seen that when the input amplitude be 1.000, the amplitude of the 2nd harmonic output amounts to 0.0971 which is 25% of that of the fundamental output, namely 0.3883. The 3rd harmonic is about 12% and the 4th harmonic is about 7%.
The extent to which aliasing might arise from the various components depends on the input frequency. If this be very low, then all the significant harmonics will be below the Nyquist frequency but, as the input frequency rises, progressively more of the components will approach, and exceed, half the sampling frequency. As an example, if the input frequency be 0.24 of the sampling frequency the 2nd, 3rd and 4th harmonics will be at 0.48, 0.72 and 0.96 of the sampling frequency. The potentially troublesome alias frequencies from them will be at 0.52, 0.28 and 0.04 of the sampling frequency, (i.e. the complement with respect to one). The normal filter following the digital-to-analogue converter should have sufficient rejection above half the sampling frequency, so that the component at 0.52 should not be too much of a problem. However, the same filter will have a negligible effect at 0.28 and 0.04 of the sampling frequency, corresponding to aliases produced by the 3rd and 4th harmonics arising in the gamma correction operation.
Probably the simplest situation to consider is where the wanted and the alias frequencies are similar and the worst of these cases is when the alias arises from the 2nd harmonic. For an input frequency at 0.33 of the sampling frequency (fs), the 2nd harmonic will be at 0.66 fs, resulting in an alias frequency of 0.34 fs. There will also be an alias at a frequency at 0.01 fs arising from the 3rd harmonic but at this stage it will be ignored.
For this input frequency, if the input amplitude be 1.000 p-p, the peak value of the largest unwanted alias component amounts to 25% of the peak value of the wanted fundamental signal. The unwanted signal is only 12 dB down on the wanted signal and this is not sufficient to prevent it being disturbing.
One solution would be to increase the sampling frequency, for example, to double it for the gamma correction operation, but this increases the complexity of the circuit and the bandwidth requirements. Also it does not remove the problem with higher-order harmonics, e.g. the third.